Textural information can play an important role in interpretation of a variety of biomedical images, such as x-rays and ultrasound recordings. We have developed a texture segmentation method using texture features obtained from a combination of spatial filters and non-linear operators. A statistical analysis has been conducted to determine the optimal combination of non-linearities. We found that the combination of transformations f(x)=lxl2 and g(x)=log(x) maximizes texture discrimination and results in a description with variances approximately constant for all feature components and texture types. We have also investigated new approaches for noise reduction and edge detection in images such as high resolution electron micrographs and ultrasound recordings. We have defined a family of discrete regularization lowpass filters (R-filters) with an adjustable scale parameter. We have shown that these filters can be implemented very efficiently through successive causal and anti-causal recursive filtering. As an application, we propose a very efficient implementation (8 multiplications + 10 additions per pixel) of the optimal Canny edge detector based on the use of a separable second-order R-filter. This latter technique is especially suited for dealing with high levels of noise, a condition that is frequently encountered in biomedical applications.